How to solve x^2 is congruent to 1 mod n

Learn how to solve x^2 is congruent to 1 mod n vs x^2 is congruent to 1 mod p. This is a the first quadratic congruence you need to know how to solve for your number theory class.

[blackpenredpen]

Which of the following is the way to spell becase?
(A) becase
(B) becose
(C) because
(D) becouse
(E) becausi

[Kartik-yiki]

Ppl who think that's a becase (4:30) do not understand bprp's genius. That is an a and u at the same time. Optimal spelling.

[nilaymarathe]

Love your work, sir.
Best of luck for the marathon.
Your 1/(1-x)

[gaurangagarwal]

You know what, before this I did not even know what congruence modulo is . Your videos are encouraging me to do more maths
:)

[mountaindewitt]

These videos are rolling in just as I'm going through modular algebra for my cryptography course

[pablofueros]

Hi! I'm stucked in this problem: Show that the int(sin(t)/(t+1)) dt from 0 to x is > 0 for all positive x. Could you try it please? Not only for me, I think it's a nice problem for the rest of the viewers studying Calc. You are awesome!!! Thanks in advance :)

[deidara_]

Very easy to see by Euler's theorem, as long as the exponent reduces to zero, you have a counter-example.

[si]

Good!!Waiting for more advanced quadratic congruences!!

[ianmoseley]

Q - if we have a 4 digit pin n1, n2, n3, n4 and we create a new pin using n1+n2 mod 10, n2+n3 mod 10, n3+n4 mod 10 and n4+n1 mod 10; what is the longest non-repeating sequence using this operation multiple times and what is the average sequence length?

[wongbob]

Please make more number theory videos with proofs!! I'm loving all these so much !

[alejrandom]

somehow the unedited parts make me like your videos even more <3

[davidgould]

I'm definitely having a "dull day": I don't get the relevance of 6 | 3·4 to showing p has to be prime in p | (x-1)(x+1) because 3·4 isn't (x-1)(x+1) with integer x.

I thought: 4 | 8 and 8 = 3² -1 = (3 - 1)(3 + 1), so 4 | (3 +1)(3 - 1)

Except we are supposed to be modulo 4, here, so 0 | 0 is trivial or undefined and 0 | (0)(2) is also nonsense, so I guess I need to brush up my modular arithmetic plugin or whatever's dropped out of my brain at this point.

Stewing my brain but loving it! Keep up the good work!

[zeeshanmehmood]

Please do more things like congruence and set theory and rings

[avijitdey]

You're crazy 🤣
Let's solve some inequalities problems 😋

[benjamimapancake]

I'm watching this instead of doing my math homework.

[CousinoMacul]

This ties in with the fact that Zmodp is a field.

[Locokillazz]

Your channel has helped me so much in my number theory class.

[PMA_ReginaldBoscoG]

Shang Chi and the Legend of Ten Rings math teacher version 😂

[davidgould]

Love the maths, but the wrist and ankle weights? Muscular development takes 2 to 3 weeks to make any difference: all you are doing a week before the marathon is getting tired. I've run 50 or so marathons and a pile of ultras (up to just over 100 miles) and have just retired from personal training (but, still, could be terribly wrong). I know you've done marathons before, and I totally understand the drive to find a few marginal gains, but the big thing in the three or four weeks before the Big Day is to get the volume of training down while keeping the frequency up: so, same schedule, but shorter. Nothing longer than 10 miles in one go in the 3-4 weeks before. Remember you're doing less: don't eat so much!

All this assumes a decent few months of progressive training beforehand.

Or you could take the approach I tend to take to marathons nowadays: just rock up and see how it goes. Obviously, it goes less quickly than before, but I'm still trying to keep the stamina up for the stupid long runs and something has to go. That something is speed: after this year's couple of 24 hour events I might focus again on moving a bit quicker. Being 58 probably doesn't help with the speed a great deal :-)

I hope the marathon goes well (or, if it was this weekend, has gone well) and look forward to your video, if you've made one this time.

[Gaark]

those weights are draining your brains man lolol